(Technically speaking, the proof of Corollary 4 in [1]} constructs a dyadic-rational stochastic matrix \(\widetilde{Q}\)  such that
\(u_n \le 0\)  iff \((\widetilde{Q}^{2n+1})_{1,4d+3} \le 1/4\) .
The desired matrix \(M\)  is then immediately obtained from \(\widetilde{Q}\)  by interchanging rows 2 and \(4d+3\) , and interchanging columns 2 and \(4d+3\) .)
